from the stack \(\mathcal {X}(d,e)\)  parametrizing pairs of representations \(A\subset B\)  with \(A\)  of dimension \(d\)  and \(B\)  of dimension \(d+e\) . In [1]}, Kontsevich–Soibelman proposed a categorification of the CoHA using categories of matrix factorizations of
the regular function \(\text{Tr}\,W\) :
\(\text{HA}(Q,W):=\bigoplus _{d\in \mathbb {N}^I} \text{MF}\left(\mathcal {X}(d), W\right).\) 
